Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T14:26:05.010Z Has data issue: false hasContentIssue false
  • English
  • Français

Space-filling zonotopes

Published online by Cambridge University Press:  26 February 2010

G. C. Shephard
G. C. Shephard
Affiliation:
University of East Anglia, Norwich NR4 7TJ, England.
Get access

Extract

By a zonotope we mean any set in Euclidean n-dimensional space Rn which can be written as a Minkowski (vector) sum of a finite number of line segments. A zonotope is a convex centrally-symmetric polytope, and all its faces are zonotopes. Familiar examples of three-dimensional zonotopes include the cube, rhombic dodecahedron, elongated dodecahedron (Figure 1) and truncated octahedron. Photographs of models of more complicated examples appear in [1, Plate II].

Type
Research Article
Information
Mathematika , Volume 21 , Issue 2 , December 1974 , pp. 261 - 269
Copyright
Copyright © University College London 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Coxeter, H. S. M.. Regular Polytopes (London-New York 1948, Second edition, 1963, Third edition, 1973).Google Scholar
2.Coxeter, H. S. M.. “The classification of zonohedra by means of projective diagrams”, J. Math. pures appliquées 41 (1962), 137–156; reprinted in Twelve Geometric Essays, (Illinois-London-Amsterdam, 1968).Google Scholar
3.McMulIen, P.. “On zonotopes”, Trans. American Math. Soc., 159 (1971), 91–109.CrossRefGoogle Scholar
4.Shephard, G. C.. “Combinatorial properties of associated zonotopes”, Canadian J. Math., 26 (1974), 302–321.CrossRefGoogle Scholar